PROC. OF THE IEEE, NOVEMBER 1998 Gradient-Based Learning Applied to Document Recognition Yann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner Abstract I. INTRODUCTION Multilayer Neural Networks trained with the backpropa- gation algorithm constitute the best example of a successful Over the last several years, machine learning techniques, Gradient-Based Learning technique. Given an appropriate particularly when applied to neural networks, have played network architecture, Gradient-Based Learning algorithms can be used to synthesize a complex decision surface that can an increasingly important role in the design of pattern classify high-dimensional patterns such as handwritten char- recognition systems. In fact, it could be argued that the acters, with minimal preprocessing. This paper reviews var availability of learning techniques has been a crucial fac- ious methods applied to handwritten character recognition and compares them on a standard handwritten digit recog- tor in the recent success of pattern recognition applica- nition task. Convolutional Neural Networks, that are specif- tions such as continuous speech recognition and handwrit- ically designed to deal with the variability of 2D shapes, are ing recognition. shown to outperform all other techniques. The main message of this paper is that better pattern Real-life document recognition systems are composed of multiple modules including field extraction, segmenta recognition systems can be built by relying more on auto- tion, recognition, and language modeling. A new learning matic learning, and less on hand-designed heuristics. This paradigm, called Graph Transformer Networks (GTN), al- is made possible by recent progress in machine learning lows such multi-module systems to be trained globally using Gradient-Based methods so as to minimize an overall per and computer technology. Using character recognition as formance meas ure. a case study, we show that hand-crafted feature extrac- Two systems for on-line handwriting recognition are de- tion can be advantageously replaced by carefully designed scribed. Experiments demonstrate the advantage of global learning machines that operate directly on pixel images. training, and the flexibility of Graph Transformer Networks A Graph Transformer Network for reading bank check is Using document understanding as a case study, we show also described. It uses Convolutional Neural Network char- that the traditional way of building recognition systems by acter recognizers combined with global training techniques manually integrating individually designed modules can be to provides record accuracy on business and personal checks. It is deployed commercially and reads several million checks replaced by a unified and well-principled design paradigm, per day. called Graph Transformer Networks, that allows training Keywords- Neural Networks, OCR, Document Recogni all the modules to optimize a global performance criterion. tion, Machine Learning, Gradient-Based Learning, Convo- Since the early days of pattern recognition it has been lutional Neural Networks, Graph Transformer Networks, Fi- known that the variability and richness of natural data, nite State Transducers be it speech, glyphs, or other types of patterns, make it almost impossible to build an accurate recognition system NOMENCLATURE entirely by hand. Consequently, most pattern recognition . GT Graph transformer. systems are built using a combination of automatic learn- . GTN Graph transformer network. ing techniques and hand-crafted algorithms. The usual . HMM Hidden Markov model. method of recognizing individual patterns consists in divid- . HOS Heuristic oversegmentation ing the system into two main modules shown in figure 1. The first module, called the feature extractor, transforms . K-NN K-nearest neighbor. .NN Neural network. the input patterns so that they can be represented by low- . OCR Optical character recognition. dimensional vectors or short strings of symbols that(a)can . PCA Principal component analysis. be easily matched or compared, and (b) are relatively in- . RBF Radial basis function. variant with respect to transformations and distortions of . RS-SVM Reduced-set support vector method. the input patterns that do not change their nature. The . SDNN Space displacement neural network. feature extractor contains most of the prior knowledge and . SVM Support vector method. is rather specific to the task. It is also the focus of most of . TDNN Time delay neural network. the design effort, because it is often entirely hand-crafted. . V-SVM Virtual support vector method. The classifier, on the other hand, is often general-purpose and trainable. One of the main problems with this ap- proach is that the recognition accuracy is largely deter The authors are with the Speech and Image Pro- cessing Services Research Laboratory, AT&T Labs- mined by the ability of the designer to come up with an Research, 100 Schulz Drive Red Bank, NJ 07701. E-mail: appropriate set of features. This turns out to be a daunt- {yann,leonb,yoshua,haffner}@research.att.com. Yoshua Bengio ing task which, unfortunately, must be redone for each new is also with the Departement d'Informatique et de Recherche Operationelle, Universite de Montreal, C.P. 6128 Succ. Centre-Ville, problem. A large amount of the pattern recognition liter- 2920 Chemin de la Tour, Montreal, Quebec, Canada H3C 3J7. ature is devoted to describing and comparing the relative￾✂✁☎✄✝✆✟✞✠✄☛✡✌☞✎✍✟✏✒✑✓✏✂✏✂✏✎✔✖✕☛✄☎✗☛✏✙✘✛✚✙✏✂✁✢✜✤✣✥✣✧✦ ✜ ★✩✫✪✭✬✯✮✟✰✲✱✴✳✶✵✶✷✪✹✸✺✰✻✬ ✼✽✰✾✪✭✩✿✱✯✮❀✱❂❁ ❃❄❅❄✯❆❇✮✟✰✻✬ ✳✫❈ ❉❈❋❊❍●❅■✰✲✱✴✳ ❏✰❍❊❑❈▲❁▼✱❅✮◆✳❖✮☛❈P✱ ◗❙❘◆❚❯❚❲❱❨❳✂❩❭❬❯❚✛❪❫❱✺❴❳❛❵✟❚✾❜❭❵◆❝❞❝❞❵✟❬✛❪❇◗✒❵◆❡❞❢✝❬❣❘❤❜❭❳✐❚❦❥◆❧♠❵❦❪❣❘✎❚❦♥❲♦♣❘✎❝rq✖❧♠s✠t❍✉✢❘✎✈✇❚❦❳✐q ①❣②④③⑥⑤✓⑦⑨⑧❶⑩✧⑤✓❷ ❸❺❹✂❻❽❼❿❾➀❻❽➁❞➂➄➃✖➅✛➆♣➃❞❹➇➅✥➁➈❻◆➆➉➃➊❼④➋❫➌➈➅❿➍✐➎➏❼❿➅✥➁➈❾➑➐✐➃❞➒➓➋➔❾→❼↔➣❭❼❿➣✐➃✌↕➇➁➄➙❿➍❛➛✂➅✥➌➈➛➇➁r➜ ➝➁r❼↔❾❽➌❛➐➞➁➈❻➝➌➈➅↔❾→❼↔➣✂➟✾➙❶➌❛➐➇➎➠❼↔❾→❼↔❹❛❼✧➃✛❼❿➣✐➃♣↕✙➃✖➎④❼❫➃➊➡✐➁➈➟❭➛✙❻❽➃❨➌➈➢✎➁➤➎✧❹➇➙❶➙❶➃✖➎✤➎✤➢⑨❹✂❻ ➥➅✥➁➄➒✙❾❽➃r➐✠❼✧➜♠➦✇➁➄➎④➃✖➒✫➧◆➃✖➁➄➅❿➐✂❾➀➐➝ ❼✥➃✖➙↔➣✂➐✂❾➩➨➇❹✐➃➄➫ ➥❾➩➭➄➃r➐✿➁➈➐✺➁➄➛✂➛✂➅✥➌➈➛✂➅↔❾❽➁r❼✥➃ ➐✐➃❶❼④➋✇➌➈➅❿➍✿➁➄➅✥➙↔➣✂❾❽❼✧➃❞➙❿❼❿❹➇➅✥➃➄➯ ➥➅✥➁➄➒✙❾➩➃❞➐➄❼✤➜⑥➦❫➁➄➎✤➃✖➒➲➧◆➃➊➁➄➅↔➐✂❾➀➐➝ ➁➈❻➝➌➈➅↔❾❽❼❿➣✂➟❭➎ ➙↔➁➈➐♣↕✙➃✇❹➇➎✤➃✖➒➳❼✥➌➵➎✤➂➇➐➄❼❿➣✐➃❞➎✧❾➩➸❶➃➏➁✛➙↔➌❛➟❭➛✙❻❽➃✖➡➔➒➇➃✖➙➊❾➑➎✧❾➩➌❛➐♣➎✧❹➇➅✥➢➺➁➄➙↔➃❦❼↔➣✐➁r❼☛➙❶➁➈➐ ➙➊❻➩➁➄➎✤➎✥❾❽➢➺➂➤➣✂❾➝➣❛➜⑥➒✙❾➑➟❙➃r➐➇➎✧❾➩➌❛➐✐➁➈❻r➛➇➁r❼✤❼✥➃✖➅↔➐➇➎✝➎✧❹➇➙↔➣➤➁➄➎❇➣✐➁➈➐➇➒➇➋✛➅↔❾❽❼✤❼✥➃❞➐➳➙↔➣✐➁➄➅✤➜ ➁➄➙❿❼✥➃✖➅❿➎↔➯➄➋➔❾❽❼❿➣✌➟➻❾➑➐✂❾➀➟❙➁➈❻✠➛✂➅✥➃✖➛✂➅✥➌➇➙↔➃✖➎✧➎✧❾➀➐➝ ➫❯➼➵➣✂❾➩➎❯➛➇➁➄➛✙➃❞➅❣➅✧➃✖➭➇❾➩➃➊➋❨➎❇➭✖➁➄➅✧➜ ❾➩➌❛❹➇➎➉➟❙➃❶❼↔➣✐➌✐➒✂➎❨➁➄➛✂➛✙❻➀❾➩➃✖➒✢❼✧➌✶➣✐➁➈➐➇➒➇➋❨➅↔❾→❼✧❼✧➃r➐✢➙↔➣✐➁➄➅✥➁➄➙❿❼✥➃✖➅➉➅✥➃❞➙↔➌➝➐✂❾❽❼❿❾➩➌❛➐ ➁➈➐➇➒✶➙❶➌❛➟❭➛➇➁➄➅✧➃❞➎➏❼↔➣✐➃❞➟✭➌❛➐➽➁❙➎④❼✧➁➈➐➇➒➇➁➄➅❿➒✶➣✐➁➈➐➇➒➇➋❨➅↔❾→❼✧❼✧➃❞➐➽➒✙❾➝❾❽❼❨➅✧➃❞➙↔➌➝➜ ➐✂❾❽❼❿❾➩➌❛➐➉❼✧➁➄➎✤➍☎➫❯➾✇➌❛➐➈➭➄➌❛❻➀❹❛❼❿❾➩➌❛➐✐➁➈❻r➆♣➃❞❹➇➅✥➁➈❻➈➆♣➃❶❼④➋✇➌➈➅❿➍❛➎❶➯✖❼↔➣✐➁r❼❀➁➄➅✥➃✇➎✧➛✙➃✖➙✖❾❽➢✓➜ ❾➑➙↔➁➈❻➑❻➩➂➞➒➇➃✖➎✥❾➝➐✐➃✖➒❙❼✧➌✌➒➇➃➊➁➈❻✙➋➔❾→❼↔➣✌❼↔➣✐➃❨➭✖➁➄➅↔❾➩➁➄↕✙❾➑❻➀❾→❼④➂➤➌➄➢☛➚✠➪✻➎✥➣✐➁➄➛✙➃❞➎↔➯➇➁➄➅✧➃ ➎✧➣✐➌r➋➔➐➻❼✥➌✒➌❛❹❛❼❿➛✙➃❞➅✧➢➺➌❛➅❿➟➶➁➈❻➀❻✎➌✠❼❿➣✐➃❞➅✛❼✧➃❞➙❿➣✂➐✂❾➑➨➇❹✐➃✖➎↔➫ ➹❨➃➊➁➈❻❽➜⑥❻➀❾❽➢➺➃❲➒➇➌✐➙✖❹✂➟✒➃r➐✠❼➘➅✥➃✖➙↔➌➝➐✂❾→❼↔❾❽➌❛➐▲➎✤➂✐➎④❼✧➃r➟❙➎❤➁➄➅✥➃❲➙↔➌✐➟❙➛☎➌➈➎④➃❞➒ ➌➄➢✒➟❙❹✂❻→❼↔❾➩➛✙❻➩➃❖➟❙➌✐➒✙❹✂❻➩➃✖➎✿❾➑➐➇➙➊❻➀❹➇➒✙❾➀➐➝➷➴➃❞❻➑➒❍➃➊➡❛❼✥➅✥➁➄➙❿❼↔❾❽➌❛➐✎➯➉➎✤➃➝➟❙➃r➐✠❼✥➁r➜ ❼❿❾➩➌❛➐✎➯❇➅✥➃❞➙↔➌➝➐✂❾❽❼❿❾➩➌❛➐✎➯❀➁➈➐➇➒➷❻❽➁➈➐➝❹✐➁➝➃➻➟❙➌➇➒➇➃❞❻➀❾➑➐➝ ➫✶➬▲➐✐➃✖➋✭❻➩➃➊➁➄➅↔➐✂❾➀➐➝ ➛➇➁➄➅✥➁➄➒✙❾➝➟➽➯☛➙↔➁➈❻➀❻❽➃❞➒ ➥➅✥➁➄➛✙➣➲➼☛➅✥➁➈➐➇➎④➢➺➌➈➅↔➟❙➃✖➅♣➆➉➃➊❼④➋❫➌➈➅❿➍✐➎❙➮➥➼❫➆➤➱❿➯☛➁➈❻→➜ ❻➩➌❞➋❨➎❯➎✧❹➇➙↔➣❭➟✒❹✂❻❽❼❿❾❽➜⑥➟❙➌✐➒✙❹✂❻➩➃❫➎✤➂✐➎④❼✧➃❞➟❭➎❀❼✧➌➤↕✙➃✛❼❿➅✧➁➈❾➀➐✐➃✖➒ ➝❻❽➌❛↕➇➁➈❻➑❻➩➂➤❹➇➎✥❾➑➐➝ ➥➅✥➁➄➒✙❾❽➃r➐✠❼✧➜♠➦✇➁➄➎④➃✖➒➲➟❙➃➊❼❿➣✐➌➇➒✂➎♣➎✤➌✶➁➄➎➉❼✧➌✿➟➻❾➀➐✂❾➑➟➻❾➩➸❶➃✌➁➈➐✫➌r➭➄➃❞➅✥➁➈❻➑❻❀➛✙➃✖➅✧➜ ➢➺➌➈➅↔➟❙➁➈➐➇➙↔➃➳➟❙➃✖➁➄➎✧❹➇➅✥➃➄➫ ➼➏➋❫➌➽➎✤➂✐➎④❼✧➃r➟❙➎➉➢➺➌➈➅➳➌❛➐❛➜⑥❻➀❾➀➐✐➃❭➣✐➁➈➐➇➒➇➋❨➅↔❾→❼↔❾➑➐➝ ➅✥➃✖➙❶➌➝➐✂❾❽❼❿❾➩➌❛➐✢➁➄➅✧➃❭➒➇➃❶➜ ➎✤➙➊➅❿❾➑↕✙➃❞➒◆➫✒✃❀➡➇➛✙➃❞➅↔❾➑➟❙➃❞➐➄❼✥➎➉➒➇➃❞➟❙➌❛➐➇➎➠❼❿➅✥➁r❼✧➃✌❼↔➣✐➃✒➁➄➒➇➭❞➁➈➐✠❼✥➁➝➃✒➌➄➢ ➝❻❽➌➈↕➇➁➈❻ ❼✥➅✥➁➈❾➀➐✂❾➑➐➝ ➯✖➁➈➐➇➒➳❼❿➣✐➃✇❐✙➃➊➡✂❾➑↕✙❾➑❻➀❾→❼④➂➉➌➄➢ ➥➅✧➁➄➛✙➣➳➼☛➅✥➁➈➐➇➎④➢➺➌❛➅❿➟❙➃❞➅❀➆♣➃❶❼④➋❫➌❛➅✥➍✐➎↔➫ ➬ ➥➅✥➁➄➛✙➣➽➼☛➅✥➁➈➐➇➎④➢➺➌❛➅❿➟❙➃❞➅✇➆♣➃❶❼④➋✇➌➈➅❿➍✒➢➺➌➈➅➉➅✧➃✖➁➄➒✙❾➑➐➝ ↕➇➁➈➐➇➍➻➙❿➣✐➃❞➙❿➍➽❾➩➎ ➁➈❻➑➎④➌✒➒➇➃❞➎✤➙❶➅↔❾➑↕✙➃✖➒◆➫➏❒♠❼➔❹➇➎④➃❞➎✛➾✇➌❛➐➈➭➄➌❛❻➀❹❛❼❿❾➩➌❛➐✐➁➈❻➇➆♣➃❞❹➇➅✥➁➈❻◆➆➉➃➊❼④➋❫➌➈➅❿➍❭➙↔➣✐➁➄➅✤➜ ➁➄➙❿❼✥➃✖➅➳➅✧➃❞➙↔➌➝➐✂❾➩➸❶➃❞➅✥➎➉➙↔➌❛➟➞↕✙❾➀➐✐➃✖➒✢➋➔❾→❼↔➣ ➝❻❽➌❛↕➇➁➈❻◆❼✥➅✥➁➈❾➀➐✂❾➑➐➝ ❼✧➃❞➙↔➣✂➐✂❾➩➨➇❹✐➃✖➎ ❼✧➌➔➛✂➅✥➌r➭✂❾➩➒➇➃❞➎☛➅✧➃❞➙↔➌➈➅❿➒➳➁➄➙❶➙➊❹➇➅✥➁➄➙↔➂➔➌✐➐➤↕✙❹➇➎✧❾➀➐✐➃✖➎✤➎✝➁➈➐➇➒✌➛✙➃✖➅❿➎✤➌❛➐✐➁➈❻✠➙↔➣✐➃✖➙❿➍✐➎↔➫ ❒♠❼✇❾➑➎❣➒➇➃✖➛✙❻➩➌❞➂➈➃✖➒❭➙↔➌❛➟➻➟❙➃✖➅❿➙➊❾➩➁➈❻➑❻➩➂➉➁➈➐➇➒❭➅✥➃➊➁➄➒✂➎❣➎④➃✖➭➄➃✖➅✥➁➈❻✂➟➻❾➀❻➑❻➀❾❽➌✐➐➤➙❿➣✐➃❞➙❿➍❛➎ ➛✙➃❞➅➉➒➇➁❞➂✠➫ ❮✇❰✤Ï↔Ð◆Ñ ⑦⑨Ò↔③♠❷ ➆♣➃❞❹➇➅✥➁➈❻✇➆➉➃➊❼④➋❫➌➈➅❿➍✐➎↔➯➏Ó➔➾➵➹➤➯❯➪➉➌✐➙➊❹✂➟❙➃r➐✠❼➻➹❨➃✖➙↔➌➝➐✂❾→➜ ❼❿❾➩➌❛➐✎➯❦❸➲➁➄➙↔➣✂❾➑➐✐➃➽➧◆➃✖➁➄➅❿➐✂❾➀➐➝ ➯ ➥➅✥➁➄➒✙❾➩➃❞➐➄❼✤➜⑥➦❫➁➄➎✤➃✖➒❖➧◆➃✖➁➄➅❿➐✂❾➀➐➝ ➯❯➾✇➌❛➐➈➭➄➌✠➜ ❻➀❹❛❼❿❾➩➌❛➐✐➁➈❻r➆➉➃r❹➇➅✥➁➈❻➄➆♣➃❶❼④➋❫➌❛➅✥➍✐➎↔➯ ➥➅✧➁➄➛✙➣➳➼☛➅✥➁➈➐➇➎④➢➺➌❛➅❿➟❙➃❞➅☛➆➉➃➊❼④➋❫➌➈➅❿➍✐➎↔➯❞Ô❇❾→➜ ➐✂❾❽❼✧➃➞Õ❛❼✧➁r❼✥➃➳➼☛➅✥➁➈➐➇➎✤➒✙❹➇➙❶➃✖➅❿➎↔➫ Ö➻×❀Ø♣Ù✙Ú❀Û◆Ü➈Ý✂Þ☛ß✝à☛Ù á➲â➤ã❲â➳ä✥å➈æ✙ç✿è✧ä❿å➄é☎ê✤ëíì➈ä✥î➻ï➊ä❞ð á➲â➤ã❨ñòâ➳ä❿å➄æ✙ç✢è✧ä❿å➄é✎ê④ëíì❛ä✧î➻ï➊ä✛é✙ï➊è④ó✇ì❛ä✧ô✟ð á✫õ♣ö➲ö÷õ➔ø✓ù✙ù✂ï➊é✫ö➲å➈ä✧ô❛ì✠ú➻î❭ì✂ù✂ï✖ûüð á✫õ➤ý➤þ✶õ➉ï➊ÿ✙ä✥ø➀ê✤è✧ø✁￾➤ì✠ú➈ï✖ä✥ê✧ï✄✂❛î➻ï➊é✐è✥å➄è✧ø➀ì➈é✝ð á✆☎✞✝➠ñ➉ñ✟☎✞✝⑥é✙ï✖å➈ä✧ï❞ê④è✛é✙ï➊ø✠✂➈ç☛✡◆ì➈ä❞ð á✫ñ♣ñ ñ➔ï➊ÿ☎ä✥å➈û☛é✙ï❶è④ó➵ì➈ä✥ô✟ð á❖ý✌☞✎✍ ý♣æ✂è✧ø✁￾➊å➈û✏￾❿ç☎å➄ä❿å✑￾❶è✧ï✖ä➵ä✥ï✒￾➊ì✑✂❛é✙ø➩è✥ø➑ì❛é✝ð á✆✓✔☞✎✕✖✓❫ä✧ø➀é✗￾➊ø➑æ☎å➈û✏￾❶ì❛î❭æ◆ì➈é☎ï➊é✐è➔å➄é☎å➈û✙✘✂ê✧ø➀ê✖ð á✆✍✛✚✔✜✢✍➉å➈ù✂ø✓å➄û✏✡✎å➈ê✧ø➀ê✇ëíÿ✙é✗￾❶è✧ø➀ì➈é✝ð á✆✍➉þ☛✝➠þ☛✣➳ö✤✍❨ï✖ù✂ÿ✥￾❶ï✖ù✦✝⑥ê✧ï❶è➔ê✧ÿ✙æ✙æ◆ì➈ä✧è➔ú➈ï✒￾❶è✧ì❛ä➵î➻ï➊è✧ç✙ì✂ù☛ð á➲þ✦✧➳ñ➉ñòþ✂æ☎å✑￾➊ï➞ù✂ø➀ê✧æ✙û✓å✑￾➊ï➊î➻ï➊é✐è❨é✙ï➊ÿ☎ä✥å➈û☛é✙ï❶è④ó➵ì➈ä✥ô✟ð á➲þ☛✣➳ö þ➇ÿ✙æ✙æ◆ì➈ä✧è➔ú➈ï★￾↔è✧ì❛ä✛î❭ï➊è✧ç✙ì✂ù☛ð á✫ã✩✧➳ñ➉ñ ã✛ø➀î➻ï➞ù✂ï➊û✓å✪✘➽é✙ï✖ÿ✙ä✥å➈û☛é✙ï❶è④ó➵ì➈ä✥ô✟ð á✫✣✬✝➠þ☛✣➳ö✭✣➉ø➀ä✤è✥ÿ☎å➄û✝ê✧ÿ✙æ✙æ◆ì➈ä✧è➔ú➈ï★￾↔è✧ì❛ä✛î❭ï➊è✧ç✙ì✂ù☛ð ✮✏✯✪✰✲✱✴✳✒✵✶✯✪✷✹✸✻✺✼✱✴✸✶✰✾✽❀✿ ✵✶✯ ✵✶✯✪✰❂❁✒❃❄✰❅✰❇❆✶✯ ✱✴❈★❉ ❊●❋✛✱✴❍✹✰❏■✥✸✶✷✴❑ ❆❅✰❅✺✶✺✶✿▲❈★❍ ❁✒✰❅✸✻▼✒✿▲❆❇✰❅✺ ◆❀✰❅✺✶✰❇✱✴✸✻❆❖✯ P✦✱✴◗❄✷✹✸❖✱❘✵✻✷✹✸✻❙❯❚ ❱✗✮❳❲❨✮ P☛✱✴◗✪✺✻❑ ◆✏✰❇✺✻✰❇✱✴✸✶❆❖✯❩❚❭❬❇❪✹❪❫❁✒❆❖✯✄✳✪❴▲❵✖❛❜✸✶✿▼❯✰❝◆✏✰❇❉❡❞❢✱✴❈✪❣❄❚✢❤❳✐❫❪❯❥✹❥✴❪★❬✹❦ ❧✗❑●❋✛✱✴✿▲❴✁♠ ♥ ❙✄✱✴❈✪❈❩❚ ❴▲✰❅✷✹❈✄◗❩❚ ❙❯✷✹✺✶✯✄✳♦✱★❚ ✯♦✱❘♣✑❈✪✰❅✸rq✴s❜✸✶✰❅✺✶✰❇✱✴✸✶❆✶✯❩❦ ✱❘✵✻✵❇❦ ❆❅✷✹❋t❦ ✉✈✷✹✺✻✯✒✳♦✱✭❞✇✰❇❈★❍✹✿▲✷ ✿▲✺①✱✴❴▲✺✻✷❝✽❀✿ ✵✻✯②✵✻✯✪✰❭❛④③✰❇❃✪✱✴✸✻✵✻✰❇❋✩✰❅❈❯✵✢❉❩⑤ ❊●❈★⑥✙✷✹✸✶❋✛✱❘✵✻✿▲⑦✒✳★✰⑧✰r✵✢❉✪✰⑨◆❀✰❅❆❖✯✪✰❅✸✻❆❖✯✪✰ ⑩❃✈③✰❅✸❖✱❘✵✻✿▲✷✹❈✪✰❅❴▲❴▲✰✹❚❄❶❳❈★✿▼❯✰❇✸✻✺✶✿ ✵✒③✰❷❉✪✰❹❸t✷✹❈❯✵✶✸✒③✰❺✱✴❴✁❚❄❻❨❦ ■❼❦♦❽★❬❇❾✹❿✛❁✄✳✪❆❅❆❯❦❢❻✇✰❇❈❯✵✻✸✶✰r❑✁➀❨✿▲❴▲❴▲✰✹❚ ❾✹➁✹❾✹❪✛❻✇✯✪✰❅❋✩✿▲❈✛❉✪✰❹❴➂✱➃✮✦✷✹✳✪✸❇❚♦❸t✷✹❈❯✵✶✸✒③✰❺✱✴❴✁❚❄➄❜✳✇③✰❅◗✑✰❅❆✹❚✑❻❢✱✴❈♦✱✴❉♦✱✩➅❳➆❯❻✫➆✹✐✄❥✒❦ ➇✪➈➉➇❿Ú☛Þ☛à✟×❀➊❇ß❀Û✎Þ❢➋í×❀Ú ý♣ú➈ï➊ä❦è✥ç✙ï➔û✓å➈ê✤è❫ê✤ï✖ú➈ï✖ä✥å➈û✦✘➈ï✖å➈ä✥ê✒➌➄î➓å✑￾❿ç☎ø➑é✙ï❨û➀ï✖å➈ä✧é☎ø➑é❼✂➳è✥ï✒￾❿ç✙é✙ø✁➍✐ÿ✙ï✖ê✒➌ æ☎å➈ä✤è✥ø✠￾➊ÿ✙û➀å➈ä✧û✠✘➽ó❨ç✙ï✖é✫å➄æ✙æ✙û➀ø➀ï✖ù✢è✧ì➓é✙ï✖ÿ✙ä❿å➄û✝é✙ï➊è④ó✇ì❛ä✧ô✂ê✒➌➇ç☎årú➈ï➤æ✙û✓å✪✘➈ï❞ù å➄é ø➀é✗￾➊ä✧ï❞å➈ê✧ø➑é❼✂❛û✙✘✲ø➑î➻æ◆ì➈ä✧è✥å➄é✐è❖ä✥ì➈û➀ï ø➀é è✧ç✙ï❑ù✂ï✖ê✧ø✙✂❛é ì➄ë➓æ☎å➄è✤è✧ï✖ä✧é ä✥ï✒￾❶ì➎✂➈é✙ø➑è✧ø➀ì➈é➷ê❺✘➇ê✤è✧ï✖î➓ê➊ð➐➏➠é➷ë⑨å✑￾❶è✒➌❯ø➩è➑￾➊ì➈ÿ✙û✓ù➒✡✎ï✢å➄ä❘✂➈ÿ✙ï❞ù❖è✥ç☎å✠è✒è✧ç✙ï årú✠å➄ø➀û➀å✑✡✙ø➀û➑ø➑è❅✘❖ì➈ë➔û➑ï❞å➄ä✥é✙ø➑é✗✂✫è✧ï★￾❿ç✙é✙ø✁➍❛ÿ☎ï✖ê➞ç✎å➈ê➓✡◆ï➊ï✖é❤å➔￾➊ä✧ÿ✥￾❶ø✓å➄û➏ë⑨å➎￾✹✝ è✧ì❛ä✢ø➀é✻è✥ç✙ï ä✧ï★￾❶ï➊é✐è✺ê✤ÿ✗￾✒￾❶ï❞ê✧ê✢ì➄ë➞æ☎å➄è✤è✥ï➊ä✥é✲ä✥ï✒￾❶ì➎✂➈é✙ø➑è✧ø➀ì➈é✻å➈æ✙æ✙û➀ø✠￾✖å♦✝ è✧ø➀ì➈é✎ê❨ê✤ÿ✗￾❿ç✿å➈ê✩￾➊ì➈é✐è✧ø➀é➇ÿ✙ì➈ÿ☎ê✛ê✧æ✎ï✖ï✒￾❿ç✢ä✧ï★￾❶ì✑✂❛é✙ø➑è✧ø➀ì➈é✢å➈é☎ù✢ç☎å➄é☎ù✙ó❨ä✧ø➑è❇✝ ø➀é❼✂➻ä✧ï★￾❶ì✑✂❛é✙ø➑è✧ø➀ì➈é✝ð ã✛ç✙ï✶î➓å➄ø➀é î➻ï✖ê✥ê✥å❄✂➈ï➓ì➈ë❨è✧ç✙ø✓ê❙æ☎å➄æ◆ï➊ä❙ø➀ê✒è✧ç☎å➄è➑✡◆ï❶è✧è✧ï➊ä❭æ☎å➄è✤è✧ï✖ä✧é ä✥ï✒￾❶ì➎✂➈é✙ø➑è✧ø➀ì➈é✺ê❺✘➇ê✤è✧ï✖î➓ê✬￾➊å➈é✫✡✎ï➓✡☎ÿ✙ø➑û➑è✬✡☛✘✿ä✧ï✖û✙✘➇ø➀é❼✂➓î➻ì➈ä✥ï➳ì❛é➲å➄ÿ✂è✥ì❄✝ î➓å✠è✥ø✠￾➤û➀ï✖å➈ä✧é✙ø➀é❼✂✥➌✙å➄é☎ù✢û➑ï❞ê✧ê➔ì➈é✿ç☎å➄é☎ù✦✝⑥ù✂ï❞ê✤ø✠✂➈é☎ï✖ù✢ç✙ï➊ÿ✙ä✥ø✓ê④è✥ø✠￾✖ê➊ð➏ã✛ç✙ø✓ê ø✓ê✶î➓å➈ù✙ï➲æ✎ì✐ê✧ê✧ø✠✡✙û➑ï➔✡❩✘➘ä✥ï✒￾➊ï➊é✐è✶æ✙ä✥ì✑✂❛ä✧ï❞ê✧ê➻ø➀é✻î➓å✑￾❿ç✙ø➀é✙ï➲û➀ï✖å➈ä✧é☎ø➑é❼✂ å➄é✎ù➒￾➊ì➈î➻æ✙ÿ✂è✥ï➊ä➤è✥ï✒￾❿ç✙é✙ì❛û➑ì➎✂✑✘❛ð➣→➉ê✧ø➑é❼✂✆￾❿ç☎å➈ä✥å➎￾↔è✥ï➊ä➤ä✧ï★￾❶ì➎✂➈é✙ø➑è✧ø➀ì➈é➷å➈ê å✢￾✖å➈ê✧ï❖ê④è✥ÿ☎ù✦✘➎➌❨ó✇ï❖ê✧ç✙ì✠ó▼è✧ç✎å✠è✢ç✎å➄é☎ù☛✝r￾❶ä❿å✠ë➺è✥ï✖ù❑ëíï✖å➄è✧ÿ✙ä✥ï➲ï✄↔✐è✥ä✥å➎￾✹✝ è✧ø➀ì➈é↕￾✖å➄é✫✡◆ï✒å➈ù✂ú✠å➈é❛è❿å❄✂❛ï➊ì➈ÿ✎ê✤û✠✘➽ä✥ï➊æ✙û✓å✑￾➊ï✖ù➐✡☛✘➙￾➊å➈ä✧ï➊ëíÿ✙û➀û✙✘✺ù✂ï✖ê✧ø✠✂➈é✙ï❞ù û➀ï✖å➄ä✥é✙ø➀é❼✂➷î➓å✑￾❿ç✙ø➀é✙ï✖ê❭è✥ç☎å✠è➽ì❛æ✎ï✖ä✥å➄è✧ï➲ù✂ø➀ä✥ï✒￾↔è✥û✙✘❤ì➈é➘æ✙ø✙↔➇ï✖û➔ø➀î➻å✑✂➈ï❞ê➊ð →➉ê✧ø➀é❼✂❺ù✂ì✦￾➊ÿ✙î➻ï➊é✐è❙ÿ✙é✎ù✂ï➊ä❿ê④è❿å➄é☎ù✙ø➑é❼✂❺å➈ê✒å➛￾➊å❛ê✤ï✶ê✤è✧ÿ✎ù✦✘✑➌❦ó➵ï✢ê✧ç✙ì✠ó è✧ç✎å✠è➏è✥ç✙ï❨è✧ä❿å➈ù✙ø➩è✥ø➑ì❛é☎å➄û✙ó✛å✪✘➞ì➈ë✇✡☎ÿ✙ø➑û✓ù✂ø➀é❼✂➞ä✥ï✒￾➊ì✑✂➈é☎ø➩è✥ø➑ì❛é❭ê❺✘✂ê④è✥ï➊î➓ê❷✡☛✘ î➓å➄é➇ÿ☎å➈û➑û✠✘➞ø➀é❛è✥ï✄✂❛ä✥å➄è✧ø➀é❼✂➤ø➑é☎ù✙ø➑ú➇ø✓ù✂ÿ☎å➄û➀û✠✘❭ù✂ï❞ê✤ø✠✂➈é☎ï✖ù❙î❭ì✂ù✂ÿ☎û➑ï❞ê➜￾➊å➈é➝✡✎ï ä✥ï➊æ✙û✓å✑￾➊ï✖ù➣✡☛✘➽å❙ÿ✙é✙ø✙➞☎ï✖ù✿å➄é✎ù➽ó➵ï➊û➀û➟✝⑥æ✙ä✥ø➑é✗￾➊ø➑æ☎û➑ï❞ù✶ù✂ï❞ê✤ø✠✂➈é✢æ☎å➄ä❿å➈ù✂ø✠✂➈î✫➌ ￾➊å➈û➑û➀ï✖ù②➠✎➡❘➢❘➤❼➥➧➦✦➡❺➢❄➨❼➩➭➫❯➯♦➡✹➲➵➳✄➡➝➸➑➳❯➺✶➻➜➯♦➡❺➼♦➩✹➌❣è✧ç☎å➄è➻å➈û➑û➀ì✠ó➔ê✌è✥ä✥å➈ø➑é☎ø➑é❼✂ å➄û➀û✙è✥ç✙ï➉î➻ì✂ù✂ÿ✙û➀ï✖ê➏è✧ì➞ì❛æ✂è✧ø➀î➻ø✙➽✖ï♣å✌✂❛û➑ì➎✡☎å➄û☎æ✎ï✖ä✤ëíì❛ä✧î➓å➄é✥￾❶ï✛￾❶ä✥ø➑è✧ï➊ä✥ø➀ì➈é✝ð þ➇ø➑é✥￾❶ï➓è✥ç✙ï➽ï✖å➈ä✧û✠✘❺ù☎å✪✘➇ê➞ì➄ë❨æ☎å✠è✧è✧ï✖ä✧é ä✥ï✒￾➊ì✑✂➈é☎ø➩è✥ø➑ì❛é❺ø➑è✒ç☎å❛ê➓✡◆ï➊ï➊é ô➇é✙ì✠ó❨é è✧ç☎å➄è➽è✧ç☎ï➲ú✠å➄ä✥ø➀å✑✡✙ø➑û➀ø➑è❅✘❑å➄é✎ù❑ä✥ø✁￾❿ç✙é✙ï✖ê✥ê➓ì➈ë➤é✎å✠è✧ÿ☎ä✥å➈û➔ù✙å✠è❿å❼➌ ✡◆ï✢ø➑è➽ê✤æ◆ï➊ï★￾❿ç✏➌❹✂➈û✠✘➇æ✙ç☎ê✒➌❣ì➈ä❭ì➄è✥ç✙ï➊ä❭è❅✘➇æ✎ï❞ê❭ì➄ë➉æ☎å➄è✤è✥ï➊ä✥é☎ê✄➌❣î➓å➈ô➈ï✿ø➩è å➄û➀î➻ì❛ê✤è❨ø➑î➻æ◆ì❛ê✥ê✤ø✠✡✙û➀ï➤è✧ì➵✡✙ÿ✙ø➀û✓ù✿å➈é✫å✑￾✄￾➊ÿ✙ä❿å✠è✧ï➤ä✥ï✒￾➊ì✑✂➈é☎ø➩è✥ø➑ì❛é✢ê❺✘➇ê✤è✧ï✖î ï➊é✐è✥ø➑ä✥ï➊û✠✘✫✡❩✘✫ç✎å➄é☎ù☛ð➉☞✇ì❛é☎ê✤ï★➍✐ÿ✙ï➊é✐è✧û✠✘✑➌✟î➻ì❛ê✤è➤æ☎å✠è✧è✧ï➊ä✥é➲ä✥ï✒￾➊ì✑✂➈é☎ø➩è✥ø➑ì❛é ê❺✘➇ê✤è✧ï✖î➓ê➉å➄ä✥ï✌✡✙ÿ✙ø➀û➑è♣ÿ☎ê✧ø➑é✗✂✶å➣￾❶ì❛î➉✡✙ø➀é☎å➄è✧ø➀ì➈é✫ì➄ë➏å➈ÿ✂è✧ì❛î➻å➄è✧ø✁￾✌û➀ï✖å➄ä✥é✦✝ ø➀é❼✂ è✧ï✒￾❿ç☎é✙ø✠➍✐ÿ✙ï❞ê✫å➄é☎ù✾ç☎å➈é☎ù☛✝r￾❶ä❿å✠ë➺è✧ï❞ù✲å➈û✙✂❛ì➈ä✥ø➩è✥ç✙î➓ê➊ð▼ã✛ç✙ï➷ÿ☎ê✤ÿ✎å➄û î➻ï❶è✥ç✙ì✂ù➞ì➄ë✎ä✧ï★￾❶ì✑✂❛é✙ø✠➽➊ø➀é❼✂➔ø➀é☎ù✂ø➀ú✐ø✓ù✂ÿ☎å➈û➇æ☎å✠è✧è✧ï➊ä✥é☎ê❜￾❶ì❛é☎ê✤ø✓ê✤è✥ê❇ø➑é❭ù✂ø➑ú➇ø✓ù☛✝ ø➀é❼✂✺è✧ç✙ï➽ê❺✘✂ê④è✥ï➊î❂ø➑é✐è✧ì✺è④ó➵ì✺î➓å➄ø➀é î➻ì✂ù✂ÿ✙û➀ï✖ê✒ê✤ç✙ì✠ó❨é ø➀é➛➞✥✂➈ÿ✙ä✥ï✫➾➈ð ã✛ç✙ï➚➞☎ä❿ê④è➤î➻ì✂ù✂ÿ✙û➀ï✑➌❀￾✖å➄û➀û➑ï❞ù✫è✧ç☎ï❙ëíï❞å✠è✥ÿ✙ä✧ï❭ï❯↔➇è✥ä✥å➎￾↔è✧ì❛ä✒➌◆è✥ä✥å➈é☎ê④ëíì❛ä✧î➓ê è✧ç☎ï♣ø➀é✙æ✙ÿ✂è✛æ☎å➄è✤è✧ï✖ä✧é✎ê➵ê✧ì✌è✥ç☎å✠è➵è✧ç✙ï✒✘➣￾➊å➈é➣✡✎ï➳ä✥ï➊æ✙ä✥ï✖ê✧ï➊é✐è✧ï❞ù➵✡☛✘➻û➑ì✠ó✔✝ ù✂ø➀î➻ï➊é☎ê✧ø➑ì❛é☎å➄û➇ú❛ï✒￾↔è✥ì➈ä❿ê✝ì❛ä❯ê✧ç✙ì➈ä✧è❯ê✤è✧ä✥ø➀é❼✂❛ê❯ì➄ë◆ê❇✘➇î➉✡◆ì➈û✓ê❀è✧ç☎å➄è✔➪üå➎➶❳￾➊å➄é ✡◆ï❭ï❞å➈ê✧ø➑û✠✘✫î➓å✠è✴￾❿ç✙ï✖ù❖ì➈ät￾❶ì➈î➻æ☎å➈ä✧ï❞ù❢➌✝å➄é✎ù➹➪➭✡✈➶♣å➈ä✧ï❭ä✥ï➊û✓å✠è✧ø➀ú➈ï✖û✙✘✺ø➀é✦✝ ú✠å➄ä✥ø➀å➈é✐è➉ó❨ø➩è✥ç❖ä✥ï✖ê✧æ✎ï★￾↔è♣è✧ì➽è✥ä✥å➈é☎ê✤ëíì➈ä✥î➻å➄è✧ø➀ì➈é☎ê➉å➄é☎ù➲ù✙ø➀ê✤è✧ì❛ä✤è✥ø➑ì❛é☎ê➔ì➈ë è✧ç☎ï➽ø➑é☎æ✙ÿ✂è✒æ☎å➄è✤è✥ï➊ä✥é☎ê✌è✥ç☎å✠è❙ù✙ì✫é✙ì➄è➉￾❿ç☎å➈é❼✂➈ï➻è✥ç✙ï➊ø➀ä✒é✎å✠è✧ÿ☎ä✧ï❛ð✢ã✛ç✙ï ëíï✖å➄è✧ÿ✙ä✥ï➔ï✄↔✐è✥ä✥å➎￾↔è✥ì➈ä❹￾❶ì❛é✐è✥å➄ø➀é☎ê❣î➻ì✐ê④è❫ì➈ë✟è✧ç✙ï➔æ☎ä✧ø➀ì➈ä➏ô➇é✙ì✠ó❨û➀ï✖ù❼✂➈ï❨å➄é☎ù ø✓ê✇ä❿å✠è✥ç✙ï➊ä➵ê✤æ◆ï✒￾➊ø➟➞✈￾➔è✥ì➞è✧ç☎ï♣è❿å➈ê✧ô✟ð❳➏⑥è✛ø➀ê✛å➈û➀ê✧ì✌è✧ç☎ï➉ëíì✦￾❶ÿ✎ê✇ì➈ë❀î➻ì❛ê✤è✇ì➈ë è✧ç☎ï✒ù✂ï✖ê✧ø✠✂➈é✺ï❯➘✟ì➈ä✧è✒➌✥✡✎ï★￾➊å➄ÿ✎ê✤ï✌ø➑è➉ø✓ê❨ì➄ë➺è✥ï➊é✫ï➊é✐è✥ø➑ä✥ï➊û✠✘✶ç☎å➈é☎ù☛✝r￾❶ä❿å✠ë➺è✥ï✖ù☛ð ã✛ç✙ï➚￾❶û✓å➈ê✥ê✤ø✙➞☎ï➊ä★➌✙ì❛é✺è✧ç✙ï❙ì➄è✧ç☎ï➊ä➉ç✎å➄é☎ù❢➌◆ø✓ê➉ì➈ë➺è✧ï➊é✆✂❛ï➊é✙ï✖ä✥å➈û➟✝⑥æ✙ÿ✙ä✥æ◆ì❛ê✧ï å➄é✎ù è✧ä❿å➄ø➀é☎å❄✡✙û➀ï➈ðòý♣é✙ï➲ì➈ë➤è✧ç✙ï➲î➓å➈ø➑é❍æ✙ä✥ì✑✡☎û➑ï✖î➻ê✶ó❨ø➩è✥ç➘è✧ç✙ø✓ê✿å➄æ✦✝ æ✙ä✥ì❛å➎￾❿ç ø✓ê✶è✧ç☎å➄è✶è✧ç☎ï❖ä✥ï✒￾❶ì➎✂➈é✙ø➑è✧ø➀ì➈é✻å➎￾✄￾➊ÿ✙ä✥å➎￾❯✘❑ø➀ê✶û➀å➈ä❺✂❛ï➊û✠✘ ù✂ï➊è✧ï✖ä❇✝ î➻ø➑é☎ï✖ù①✡☛✘❺è✧ç✙ï✿å❄✡✙ø➀û➑ø➑è❅✘ ì➄ë❨è✧ç☎ï✢ù✂ï❞ê✤ø✠✂➈é✙ï✖ä✌è✧ì➛￾❶ì➈î➻ï✢ÿ✙æ ó❨ø➩è✥ç❤å➄é å➄æ☎æ✙ä✧ì❛æ✙ä✥ø➀å➄è✧ï➞ê✧ï❶è➉ì➈ë❯ëíï❞å✠è✥ÿ✙ä✧ï❞ê➊ð➔ã✛ç☎ø➀ê➔è✧ÿ✙ä✥é☎ê➔ì❛ÿ✂è➉è✥ì➣✡◆ï❙å➓ù✙å➈ÿ✙é✐è❇✝ ø➀é❼✂➳è✥å➈ê✧ô➞ó❨ç✙ø✁￾❿ç✏➌➄ÿ☎é✂ëíì➈ä✧è✧ÿ✙é✎å✠è✧ï✖û✙✘➎➌➈î❙ÿ☎ê④è❷✡◆ï❨ä✧ï❞ù✂ì➈é☎ï✇ëíì❛ä❦ï✖å✑￾❿ç❭é✙ï✖ó æ✙ä✥ì✑✡✙û➀ï➊î✺ð✞✕òû✓å➄ä❘✂➈ï✒å➈î❭ì❛ÿ✙é✐è➉ì➄ë❣è✥ç✙ï❭æ☎å✠è✧è✧ï➊ä✥é➲ä✥ï✒￾➊ì✑✂➈é☎ø➩è✥ø➑ì❛é✿û➀ø➑è✧ï➊ä❺✝ å✠è✥ÿ✙ä✥ï❙ø✓ê➤ù✂ï➊ú❛ì➄è✧ï❞ù✫è✥ì✿ù✂ï❞ê❺￾➊ä✧ø✠✡✙ø➀é❼✂✺å➄é☎ù➛￾❶ì➈î➻æ☎å➈ä✧ø➀é❼✂✶è✧ç✙ï➻ä✥ï➊û✓å✠è✧ø➀ú➈ï